Question
Cjavascript:void(0)alculate and compare the surface area of sphere A, which has a radius of 4in and sphere B which has a radius of 10 in. The formula for the surface area of a sphere is 4πr2
4
𝜋
𝑟
2
(1 point)
Responses
Sphere A has a surface area of 64π in2
64
𝜋
𝑖
𝑛
2
and sphere B has a surface area of 400π in2
400
𝜋
𝑖
𝑛
2
, meaning sphere B's surface area is 6.25 times as large as sphere A's.
Sphere A has a surface area of 64π in2
64
𝜋
𝑖
𝑛
2
and sphere B has a surface area of 400π in2
400
𝜋
𝑖
𝑛
2
, meaning sphere B's surface area is 6.25 times as large as sphere A's.
4
𝜋
𝑟
2
(1 point)
Responses
Sphere A has a surface area of 64π in2
64
𝜋
𝑖
𝑛
2
and sphere B has a surface area of 400π in2
400
𝜋
𝑖
𝑛
2
, meaning sphere B's surface area is 6.25 times as large as sphere A's.
Sphere A has a surface area of 64π in2
64
𝜋
𝑖
𝑛
2
and sphere B has a surface area of 400π in2
400
𝜋
𝑖
𝑛
2
, meaning sphere B's surface area is 6.25 times as large as sphere A's.
Answers
GPT-4o mini
To calculate the surface area of the spheres, we can use the formula for the surface area of a sphere, which is:
\[
SA = 4\pi r^2
\]
### For Sphere A (radius = 4 inches):
\[
SA_A = 4\pi (4)^2
\]
\[
SA_A = 4\pi (16)
\]
\[
SA_A = 64\pi \, \text{in}^2
\]
### For Sphere B (radius = 10 inches):
\[
SA_B = 4\pi (10)^2
\]
\[
SA_B = 4\pi (100)
\]
\[
SA_B = 400\pi \, \text{in}^2
\]
### Comparison of Surface Areas:
- Sphere A has a surface area of \( 64\pi \, \text{in}^2 \)
- Sphere B has a surface area of \( 400\pi \, \text{in}^2 \)
To find out how many times larger the surface area of sphere B is compared to sphere A:
\[
\frac{SA_B}{SA_A} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25
\]
### Conclusion:
Sphere A has a surface area of \( 64\pi \, \text{in}^2 \) and sphere B has a surface area of \( 400\pi \, \text{in}^2 \), meaning sphere B's surface area is **6.25 times as large as sphere A's**.
\[
SA = 4\pi r^2
\]
### For Sphere A (radius = 4 inches):
\[
SA_A = 4\pi (4)^2
\]
\[
SA_A = 4\pi (16)
\]
\[
SA_A = 64\pi \, \text{in}^2
\]
### For Sphere B (radius = 10 inches):
\[
SA_B = 4\pi (10)^2
\]
\[
SA_B = 4\pi (100)
\]
\[
SA_B = 400\pi \, \text{in}^2
\]
### Comparison of Surface Areas:
- Sphere A has a surface area of \( 64\pi \, \text{in}^2 \)
- Sphere B has a surface area of \( 400\pi \, \text{in}^2 \)
To find out how many times larger the surface area of sphere B is compared to sphere A:
\[
\frac{SA_B}{SA_A} = \frac{400\pi}{64\pi} = \frac{400}{64} = 6.25
\]
### Conclusion:
Sphere A has a surface area of \( 64\pi \, \text{in}^2 \) and sphere B has a surface area of \( 400\pi \, \text{in}^2 \), meaning sphere B's surface area is **6.25 times as large as sphere A's**.